A178900 - OEIS

A178900

First nonzero value of (a^(p-1) - 1) mod p^2, for a > 0 coprime to the n-th Wieferich prime p.

%I #7 Sep 07 2023 07:14:43

%S 341016,24577

%N First nonzero value of (a^(p-1) - 1) mod p^2, for a > 0 coprime to the n-th Wieferich prime p.

%C It is believed that a(n) = (3^(p-1) - 1) mod p^2 for all n, where p = A001220(n).

%C See additional comments, references, links and cross-references in A001220.

%H A. Ostafe and I. Shparlinski (2010), <a href="http://arxiv.org/abs/1001.1504">Pseudorandomness and Dynamics of Fermat Quotients</a>, arXiv:1001.1504 [math.NT], 2010.

%F a(n) = (A178815(A000720(p))^(p-1) - 1) mod p^2, where p = A001220(n).

%F a(n) mod p = A178844(A000720(p)), where p = A001220(n).

%e The first Wieferich prime is 1093 and a^1092 - 1 mod 1093^2 = 0, 0, 341016 for a = 1, 2, 3, so a(1) = 341016.

%Y Cf. A001220, A178815, A178844.

%K bref,hard,more,nonn

%O 1,1

%A _Jonathan Sondow_, Jun 23 2010